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XXII International Cartographic Conference, A Coruña, July 9-16th, 2005 1
Modelling Cartographic Relations for Categorical Maps
Moritz Neun and Stefan Steiniger
University of Zürich, Department of Geography
Swiss National Science Foundation Project: DEGEN
{neun, sstein}@geo.unizh.ch
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Outline
1. Motivation
2. Introducing Relations
3. Modelling Horizontal & Vertical Relations
4. Outlook
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1. Motivation
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Thematic (Categorical) Maps
Most research in generalization on topographic maps
majority of maps are of thematic nature (categorical, GIS, facilities, networks, POI ...)
focus on thematic mapswith polygons ina generic approach
Examples: geology, land-use, statistics, administration
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Motivation
Generalization should preserve the typical and emphasise specifics.
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Motivation
Generalization should preserve the typical and emphasise specifics.
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2. Introducing Relations
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What is considered as a relation?
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What is considered as a relation?
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What is considered as a relation?
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What is considered as a relation?
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What is considered as a relation?
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3. Horizontal & Vertical Relations
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Horizontal & Vertical Relations
Horizontal relations
of map objects exist within one specific scale or level of detail (LOD) and represent common structural properties.
horizontal relations
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Relation Types topologic neighbour
frequency,
area statistics
compactness,
area size, distance
orientation =>
meso structure?
Inter-thematic
structurefor aggregation (are blue
soil classes of same familly?)
=> Semantic similarity
Geometry
Topology
Structure
Statistics and Density
Semantics
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Horizontal Relations
Horizontal Relations
geometrical topological structural statistical semantical
position
size
orientation
shape
structure
order of neig-bourhood
9IM
ring
meso structure
background/foreground
macro structure
Inter-thematic
statistical baseparameters
area relations
categoricalrelations
similarity
priority
resistance/ attraction
nature of origin
orientationpatterns
causal and logicrelationsdiversity
metrics
configurationmetrics
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Topological Properties
Topologic structure:- Island (in other polygon or background)
- Island cluster- Landscape (complete tesselation)
Ring model relationisland
island cluster
landscape
ring modelwith three levels
Topologic neighbourhood
Nine-Intersection Model (9IM) : e.g. overlap, touch, contain, ...
neigbourhood
l1l2
l3
A 1
2
2
3
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Structural Properties
visible patterns gestalt theory meso structures
A proximity groupings
B similarity (size, shape, orientation)
C grouping by type
D parallelism
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Horizontal & Vertical Relations
Horizontal relations
of map objects exist within one specific scale or level of detail (LOD) and represent common structural properties.
horizontal relations
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Horizontal & Vertical Relations
Horizontal relations
of map objects exist within one specific scale or level of detail (LOD) and represent common structural properties.
horizontal relations vertical relations
1:25k
1:200k
Vertical relations
are links between single map objects or groups of map objects between different map scales and LODs.
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vertical relations
map object relations LOD relations
semantic structural
neigbourhoodmatrix
diversity
configuration
similarity
legend
type priorities
causal & logic
identity relation1:1
group relationn:m
simplification
smoothing
enlargement
exaggeration
collapse
aggregation(alignment, cluster)
amalgamation(cluster)
typification(cluster, alignment)
symbolization
displacement
partitioning
(e.g. by alignments)
relations between propertiesof whole LODs
e.g. semantic similarity or type prioritiesfor aggregation
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vertical relations
map object relations LOD relations
semantic structural
neigbourhoodmatrix
diversity
configuration
similarity
legend
type priorities
causal & logic
identity relation1:1
group relationn:m
simplification
smoothing
enlargement
exaggeration
collapse
aggregation(alignment, cluster)
amalgamation(cluster)
typification(cluster, alignment)
symbolization
displacement
partitioning
(e.g. by alignments)
relations between single map objects or groups matching and formalisation of thegeometrical, topological and semantical outcomewith abstract generalization operators
abstract procedural knowledge
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Vertical Identity Relations 1:1
x
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Vertical Identity Relations 1:1
x
A Coruña
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Vertical Group Relations n:m
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Enrichment of Relations
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Vertical Relation Properties
enrich relations with additional information
relation properties
semantic properties geometric properties topological properties
size / position
shape
orientation
neigbourhood
intersection type
structure
statistics
resistance /attraction
configuration(island, landscape)
containment(in, ring model)
change originator
threshold level
type change
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4. Outlook
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Using Relations
• Improve automated generalisation (horizontal relations)• choice of appropriate algorithms
• more information about parameters for algorithms
• better evaluation of results
• Interpolation of intermediate scale levels
(Cecconi 2003) e.g. in combination with morphing
• Incremental updating of lower detailed LODs (Kilpeläinen
and Sarjakoski 1995)
• Training and use of learning algorithms (inductive, neuronal)
by analyzing relations and properties (Weibel et al. 1995
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Thanks for your attention!
Any questions, suggestions or comments?
maps: • Flood hazard map: www.nlfb.de, • China –language region map: www.hphein.de/, • snow depth map: http://www.slf.ch/swiss-snow/hstopodc.html, • soil map „Littau“: IKA, ETHZ, Switzerland
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Matching
1:25‘000 1:200‘000
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Project DEGEN
Purpose: • data enrichment with relations• modeling of enriched data• exploitation of enriched data
Focus: • thematic vector maps
Goals/Questions: • types of “vertical” relations betweenmap objects on different LODs?
• modelling and representing in a MRDB?• matching of map objects in two LODs and
acquisition relations and their attributes?• management and deployment of relations?• usefulness of vertical relations for the
creation of intermediate LODs?• usefulness of the same relations for
incremental generalization?
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Vertical Relationsvertical relations
map object relations LOD relations
semantic structural
neigbourhoodmatrix
diversity
configuration
similarity
legend
type priorities
causal & logic
identity relation1:1
group relationn:m
simplification
smoothing
enlargement
exaggeration
collapse
aggregation(alignment, cluster)
amalgamation(cluster)
typification(cluster, alignment)
symbolization
displacement
partitioning
(e.g. by alignments)